🧮 algebra

1. Stating the problem: We need to separate the given real numbers into rational and irrational numbers and explain the reasoning. 2. Definition reminder:

1. The problem is to rationalise the denominator of the fraction \( \frac{\sqrt{2} + 10}{2 - \sqrt{2}} \) and express the answer in the form \( a + b\sqrt{2} \). 2. To rationalise

1. **State the problem:** Simplify the expression $$(2 + 2\sqrt{27})(3\sqrt{3} - 1)$$. 2. **Simplify the terms inside the expression:** First, simplify $\sqrt{27}$. Since $$27 = 9

1. Let's create a simple algebraic problem: Solve for $x$ in the equation $$2x + 5 = 13$$. 2. To solve for $x$, first subtract 5 from both sides to isolate the term with $x$:

1. Problem: Describe the set $A$ which contains all even numbers between 2 and 10. Step 1: Identify even numbers between 2 and 10.

1. The problem asks us to explain what an equivalence relation is and its use with an example. 2. An equivalence relation on a set is a relation that satisfies three properties:

1. **Problem Statement:** Expand and simplify the expression $$(x+1)(x+2)(x+5)$$. 2. **Step 1:** First, expand the first two binomials $$(x+1)(x+2)$$.

1. समस्या सांगितली आहे की दोन संख्यांच्या रूपात $7 + 4A$ आणि $5 + 2B$ यांचा गुणाकार 98537 अशी संख्या मिळते. \n2. या 98537 या संख्येचा दशकस्थानाचा अंक आपण लक्षात घेऊ, म्हणजेच ही संख

1. The problem is to expand and simplify the expression $ (x+1)(x+2)(x+3) $. 2. First, multiply the first two binomials: $ (x+1)(x+2) = x^2 + 2x + x + 2 = x^2 + 3x + 2 $.

1. The problem is to simplify the expression $$\frac{9x^2 - 16}{3x + 4}.$$\n\n2. Start by factoring the numerator, which is a difference of squares: $$9x^2 - 16 = (3x)^2 - 4^2 = (3

1. प्रश्न समजून घेऊया: \(|x| = -x\) असं दिलं आहे. आपल्याला \(x\) चं कोणतं मूल्य असू शकतं हे शोधायचं आहे. 2. पूर्णांक \(x\) साठी पूर्णांक गुणधर्म पाहूया.

1. Stating the problem: We are given two functions f(x) = 7x + 6

1. We are asked to factorize the expression $$9c^2 - 12cd + 4d^2 + 10cd^2 - 15c^2d$$.

1. The problem is to graph the linear equation $y=3x+1$. 2. The slope is $3$ and the y-intercept is $1$. This means the line crosses the y-axis at the point $(0,1)$ and rises 3 uni

1. **State the problem:** Jomar wants to make 1-liter bottles of iced coffee mix using 3/4 liter of brewed coffee and 1/2 liter of milk per bottle. He has 3 liters of coffee and 2

1. **State the problem:** Solve the inequality $$\frac{1}{3^x + 1} + \frac{1}{3^x - 3} \leq 0.$$ 2. **Combine the fractions:** Find a common denominator and combine:

1. **State the problem:** We have a set $A$ of all lines in the $xy$-plane and a relation $R$ on $A$ defined by $R = \{(L_1, L_2) : L_1 \parallel L_2\}$. We need to show that $R$ i

1. **State the problem:** Coach Leo scheduled \(\frac{2}{5}\) hours for dribbling drills and \(\frac{1}{4}\) hour for team scrimmage. The gym is available for 1 hour. We need to de

1. Stating the problem: Solve the inequality $$\frac{1}{3^x} + 1 + \frac{1}{3^x} - 3 \leq 0$$. 2. Combine like terms: $$\frac{1}{3^x} + \frac{1}{3^x} = 2 \cdot \frac{1}{3^x}$$.

1. **Stating the problem:** Solve the inequality $$\left(\frac{1}{3^x}+1\right) + \frac{1}{3^x} - 3 \leq 0.$$\n\n2. **Rewrite the inequality:** Combine like terms involving $\frac{

1. The problem is to simplify the expression $\left(\frac{1}{3^x}+1\right)+\frac{1}{3^x}-3$. 2. Rewrite the expression as $\frac{1}{3^x} + 1 + \frac{1}{3^x} - 3$.